Please solve all questions thanks 8. For each of the following statements, deter

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Please solve all questions thanks

8. For each of the following statements, determine whether it is true or false (circle the [14] answer; you don't need to show any work). (a) True or False: Switching two rows in a square matrix preserves its rank. (b) True or False: Switching two rows in a square matrix preserves its determinant. (c) True or False: Two matrices can be multiplied by each other if and only if their sizes are the same. (d) True or False: det(AB) det (A)det (B) (e) True or False: (AB) (A) (B) 1. (f) True or False: A homogeneous system of linear equations always has a solution (g) True or False: The system Az b has NO solution if rank A rank A lbl where CA Ib is the augmented matrix. 9. Let 1 15 2 8 Find each of the following matrices (a) Matrix E1 that adds -2R1 to R2 of A to get B. (b) Matrix E2 that divides R2 of B by -22 to get C. (c) Matrix E3 that adds -15R2 to R1 to get D

Explanation / Answer

a). True

b).False

c).False

d).true

e).false

f).True

g).false

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